Normal elements of noncommutative Iwasawa algebras over \(\mathrm{SL}_{3}(\mathbb{Z}_{p})\) (Q670962)

Let \(p\) be a prime integer and let \(\mathbb{Z}_p\) be the ring of \(p\)-adic integers. Using a purely computational approach, the authors proved in the main result of the reviewed paper, namely Theorem 4.1, that each non-zero normal element of a noncommutative Iwasawa algebra over the special linear group \(\mathrm{SL}_3(\mathbb{Z}_p)\) is a unit. This gives a positive answer to an open question in [the second author and \textit{D. Bian}, Int. J. Algebra Comput. 23, No. 1, 215 (2013; Zbl 1267.20009)] and makes up for an earlier mistake in [the second author and \textit{D. Bian}, Int. J. Algebra Comput. 20, No. 8, 1021--1039 (2010; Zbl 1220.20003)] simultaneously. The paper under review is well written and structured with a good organization of the computations.